title: Limitations in the application of the Gibbs equation to anionic surfactants at the air/water surface: sodium dodecylsulfate and sodium dodecylmonooxyethylenesulfate above and below the CMC.
abstract: This is a second paper responding to recent papers by Menger et al. and the ensuing discussion about the application of the Gibbs equation to surface tension (ST) data. Using new neutron reflection (NR) measurements on sodium dodecylsulfate (SDS) and sodium dodecylmonooxyethylene sulfate (SLES) above and below their CMCs and with and without added NaCl, in conjunction with the previous ST measurements on SDS by Elworthy and Mysels (EM), we conclude that (i) ST measurements are often seriously compromised by traces of divalent ions, (ii) adsorption does not generally reach saturation at the CMC, making it difficult to obtain the limiting Gibbs slope, and (iii) the significant width of micellization may make it impossible to apply the Gibbs equation in a significant range of concentration below the CMC. Menger et al. proposed ii as a reason for the difficulty of applying the Gibbs equation to ST data. Conclusions i and iii now further emphasize the failings of the ST-Gibbs analysis for determining the limiting coverage at the CMC, especially for SDS. For SDS, adsorption increases above the CMC to a value of 10 × CMC, which is about 25% greater than at the CMC and about the same as at the CMC in the presence of 0.1 M NaCl. In contrast, the adsorption of SLES reaches a limit at the CMC with no further increase up to 10 × CMC, but the addition of 0.1 M NaCl increases the surface excess by 20-25%. The results for SDS are combined with earlier NR results to generate an adsorption isotherm from 2 to 100 mM. The NR results for SDS are compared to the definitive surface tension (ST) measurements of EM, and the surface excesses agree over the range where they can safely be compared, from 2 to 6 mM. This confirms that the anomalous decrease in the slope of EM's σ - ln c curve between 6 mM and the CMC at 8.2 mM results from changes in activity associated with a significant width of micellization. This anomaly shows that it is impossible to apply the Gibbs equation usefully from 6 to 8.2 mM (i.e., the lack of knowledge of the activity in this range is the same as above the CMC (8.2 mM)). It was found that a mislabeling of the original data in EM may have prevented the use of this excellent ST data as a standard by other authors. Although NR and ST results for SDS in the absence of added electrolyte show that the discrepancies can be rationalized, ST is generally shown to be less accurate and more vulnerable to impurities, especially divalent ions, than NR. The radiotracer technique is shown to be less accurate than ST-Gibbs in that the four radiotracer measurements of the surface excess are consistent neither with each other nor with ST and NR. It is also shown that radiotracer results on aerosol-OT are likely to be incorrect. Application of the mass action (MA) model of micellization to the ST curves of SDS and SLES through and above the CMC shows that they can be explained by this model and that they depend on the degree of dissociation of the micelle, which leads to a larger change in the mean activity, and hence the adsorption, for the more highly dissociated SDS micelles than for SLES. Previous measurements of the activity of SDS above the CMC were found to be semiquantitatively consistent with the change in mean activity predicted by the MA model but inconsistent with the combined ST, NR, and Gibbs equation results.
authors.affiliation: Physical and Theoretical Chemistry Laboratory, South Parks Road, University of Oxford, Oxford OX1 3QZ, UK.
authors.forename: Hui
authors.initials: H
authors.lastname: Xu
authors.forename: Pei Xun
authors.initials: PX
authors.lastname: Li
authors.forename: Kun
authors.initials: K
authors.lastname: Ma
authors.forename: Robert K
authors.initials: RK
authors.lastname: Thomas
authors.forename: Jeffrey
authors.initials: J
authors.lastname: Penfold
authors.forename: Jian Ren
authors.initials: JR
authors.lastname: Lu